Google Workspace Skill

Comprehensive MCP integration for all Google Workspace services.

Denotation

Google Workspace tasks map to functional invariants, resulting in consistent email, file, calendar, and task states under Narya condensation and GF(3) conservation.

The skill reaches a fixed point when all pending operations complete with no H¹ obstructions (gluing failures), and thread/folder trit sums are conserved modulo 3.

Formal Contract

Effect: Google Workspace → State × Trit
Invariant: ∀ closed workflow: Σ(trit) ≡ 0 (mod 3)
Denotation: ⟦GW⟧ = lim_{n→∞} Condense(Op_n(...Op_1(S_0)))

Required Parameter

All tools require user_google_email - the user's Google email address.

Services Overview

📧 Gmail (MINUS -1: Validator)

Tool	Description
`search_gmail_messages`	Search with Gmail query syntax
`get_gmail_message_content`	Get full message content
`get_gmail_messages_content_batch`	Batch get (max 25)
`get_gmail_thread_content`	Get full conversation thread
`send_gmail_message`	Send email (supports replies)
`draft_gmail_message`	Create draft (supports replies)
`modify_gmail_message_labels`	Add/remove labels (archive, delete)
`batch_modify_gmail_message_labels`	Bulk label operations
`list_gmail_labels`	List all labels with IDs
`manage_gmail_label`	Create/update/delete labels

Query syntax examples:

from:user@example.com - From specific sender
is:unread - Unread messages
has:attachment - Has attachments
after:2024/01/01 - Date filters

📁 Drive (ERGODIC 0: Coordinator)

Tool	Description
`search_drive_files`	Search files by query
`list_drive_items`	List folder contents
`get_drive_file_content`	Get file content (text extraction)
`get_drive_file_download_url`	Get download URL
`create_drive_file`	Create new file
`update_drive_file`	Update metadata
`share_drive_file`	Share with users/groups/anyone
`batch_share_drive_file`	Bulk sharing
`get_drive_file_permissions`	Check permissions
`get_drive_shareable_link`	Get shareable link
`remove_drive_permission`	Revoke access
`transfer_drive_ownership`	Transfer file ownership

📅 Calendar (PLUS +1: Executor)

Tool	Description
`list_calendars`	List user's calendars
`get_events`	Get events (by ID or time range)
`create_event`	Create new event
`modify_event`	Update existing event
`delete_event`	Delete event

Event creation options:

add_google_meet: true - Add Meet link
attendees: ["email1", "email2"] - Invite attendees
reminders: [{"method": "popup", "minutes": 15}] - Custom reminders
transparency: "transparent" - Show as available

📄 Docs (MINUS -1)

Tool	Description
`search_docs`	Search Google Docs
`list_docs_in_folder`	List docs in folder
`create_doc`	Create new document
`get_doc_content`	Get document content
`modify_doc_text`	Insert/replace/format text
`find_and_replace_doc`	Find and replace
`insert_doc_image`	Insert image
`insert_doc_elements`	Insert table/list/page break
`create_table_with_data`	Create populated table
`inspect_doc_structure`	Get document structure
`debug_table_structure`	Debug table layout
`update_doc_headers_footers`	Update headers/footers
`batch_update_doc`	Multiple operations
`export_doc_to_pdf`	Export to PDF

📊 Sheets (ERGODIC 0)

Tool	Description
`list_spreadsheets`	List spreadsheets
`create_spreadsheet`	Create new spreadsheet
`get_spreadsheet_info`	Get spreadsheet metadata
`create_sheet`	Add new sheet
`read_sheet_values`	Read cell range
`modify_sheet_values`	Write/update/clear cells

Range syntax: Sheet1!A1:D10 or A1:Z1000

📽️ Slides (PLUS +1)

Tool	Description
`create_presentation`	Create new presentation
`get_presentation`	Get presentation details
`get_page`	Get slide details
`get_page_thumbnail`	Get slide thumbnail
`batch_update_presentation`	Apply updates

📋 Forms

Tool	Description
`create_form`	Create new form
`get_form`	Get form details
`list_form_responses`	List responses
`get_form_response`	Get specific response
`set_publish_settings`	Update publish settings

✅ Tasks

Tool	Description
`list_task_lists`	List all task lists
`get_task_list`	Get task list details
`create_task_list`	Create new list
`update_task_list`	Rename list
`delete_task_list`	Delete list
`list_tasks`	List tasks in list
`get_task`	Get task details
`create_task`	Create task
`update_task`	Update task
`delete_task`	Delete task
`move_task`	Move task (position/list)
`clear_completed_tasks`	Clear completed

💬 Chat

Tool	Description
`list_spaces`	List Chat spaces
`get_messages`	Get messages from space
`search_messages`	Search messages
`send_message`	Send message to space

🔍 Custom Search

Tool	Description
`search_custom`	Programmable Search Engine
`search_custom_siterestrict`	Site-restricted search
`get_search_engine_info`	Get search engine config

💬 Comments (All Doc Types)

Tool	Description
`read_document_comments`	Read doc comments
`create_document_comment`	Add doc comment
`reply_to_document_comment`	Reply to comment
`resolve_document_comment`	Resolve comment
`read_spreadsheet_comments`	Read sheet comments
`create_spreadsheet_comment`	Add sheet comment
`read_presentation_comments`	Read slide comments
`create_presentation_comment`	Add slide comment

GF(3) Triadic Workflow

MINUS (-1): Validation/Reading
├── search_gmail_messages
├── get_doc_content
├── read_sheet_values
└── list_drive_items

ERGODIC (0): Coordination/Metadata
├── get_spreadsheet_info
├── list_calendars
├── inspect_doc_structure
└── get_drive_file_permissions

PLUS (+1): Execution/Writing
├── send_gmail_message
├── create_event
├── modify_sheet_values
└── create_drive_file

Common Workflows

Email Management

# Search → Read → Reply
messages = search_gmail_messages(query="from:boss is:unread")
content = get_gmail_message_content(message_id=messages[0].id)
send_gmail_message(
    to="boss@company.com",
    subject="Re: " + content.subject,
    body="Response...",
    thread_id=content.thread_id,
    in_reply_to=content.message_id
)

Document Creation

# Create → Inspect → Add Table
doc = create_doc(title="Report")
structure = inspect_doc_structure(document_id=doc.id)
create_table_with_data(
    document_id=doc.id,
    index=structure.total_length,
    table_data=[["Header1", "Header2"], ["Data1", "Data2"]]
)

Calendar Scheduling

# Check availability → Create event with Meet
events = get_events(
    time_min="2024-12-26T09:00:00Z",
    time_max="2024-12-26T17:00:00Z"
)
create_event(
    summary="Team Sync",
    start_time="2024-12-26T14:00:00Z",
    end_time="2024-12-26T15:00:00Z",
    attendees=["team@company.com"],
    add_google_meet=True
)

File Sharing

# Share with expiration
share_drive_file(
    file_id="abc123",
    share_with="contractor@example.com",
    role="writer",
    expiration_time="2025-01-15T00:00:00Z"
)

Authentication

If tools fail with auth errors, use:

start_google_auth(service_name="gmail|drive|calendar|docs|sheets|slides|forms|tasks|chat")

Tips

Batch operations - Use batch tools for multiple items
Table creation - Always call inspect_doc_structure first to get safe index
Email threading - Include thread_id, in_reply_to, references for proper replies
Drive shared drives - Use drive_id parameter for shared drive operations
Calendar attachments - Use Drive file URLs or IDs for event attachments

Related Skills (Backlinks)

Skill	Trit	Integration
finder-color-walk	0	Drive files ↔ local Finder GF(3) coloring via `drive_color_walk.py`
gay-mcp	+1	SplitMix64 deterministic colors for file organization
triad-interleave	+1	Schedule Drive operations in GF(3)-balanced triplets
bisimulation-game	-1	Verify Drive state equivalence across agents

Triadic Integration Pattern

google-workspace (ERGODIC 0) ─── Coordinator
        │
        ├── finder-color-walk (0) ─── File coloring bridge
        │       └── drive_color_walk.py
        │
        ├── gay-mcp (+1) ─── Color generation
        │       └── SplitMix64 seeds → GF(3) trits
        │
        └── bisimulation-game (-1) ─── State verification
                └── Attacker/Defender/Arbiter protocol

GF(3) Check: 0 + 0 + 1 + (-1) = 0 ✓

Invariant Set

Invariant	Definition	Verification
`NoDuplication`	Each item (message, event, file) resides in exactly one triadic queue	Queue intersection = ∅
`RouteInvariance`	`route(item) = agent_of(trit(item))` always	For all items, routing is deterministic
`ThreadConservation`	Thread trit sum ≡ 0 (mod 3) at cycle close	`verify_h1_obstruction()` returns no violations
`ClosedWorkflowBalance`	Any complete workflow has Σ trits = 0	GF(3) conservation check

Narya Compatibility

Field	Definition	Example
`before`	Raw input from Google APIs	`{"messages": [...], "files": [...]}`
`after`	Transformed interactions with GF(3) trits	`[{id, trit, verb, thread_id}]`
`delta`	Change in triadic queue state	`{added: 3, removed: 1, trit_sum_delta: +1}`
`birth`	Initial unprocessed state	Empty queues, no interactions
`impact`	1 if equivalence class changed, 0 otherwise	Used for ANIMA detection

Condensation Policy

Trigger: When 10 consecutive operations yield no change in equivalence classes.

def should_condense(history: List[State], threshold: int = 10) -> bool:
    if len(history) < threshold:
        return False
    recent = history[-threshold:]
    return all(equiv(s) == equiv(recent[0]) for s in recent)

Action: Collapse queue state into condensed fingerprint, archive processed items.

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Graph Theory

networkx [○] via bicomodule
- Universal graph hub

Bibliography References

general: 734 citations in bib.duckdb

Cat# Integration

This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:

Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826

GF(3) Naturality

The skill participates in triads satisfying:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.

google-workspace